The cat -- hired in a blaze of publicity -- fastidiously chose between bowls of food decked with national flags on Thursday, picking between Australia and Cameroon which were to play later in the day.
Australia came first by a whisker after Achilles jumped onto the bowl.
He previously correctly predicted that Russia would beat New Zealand last week.
Known as Akhill, the Russian name for Greek mythological hero Achilles, he is one of some 50 feline guardians at the revered classical art museum and former tsarist Winter Palace.
"We chose Akhill for this role due to his very sociable and stress-resistant nature," said Maria Khaltunen, who is responsible for the museum's cats.
The white-furred blue-eyed cat aged around one will not be suspectible to a quiet word from either side, since he is deaf, Khaltunen said.
"That means it's impossible to attract his attention with some sound at the moment of choice," she said.
The cat follows a long line of animal forecasters for popular sports events including a sheep, a guinea pig, a raccoon.
Most famously, Paul the psychic German octopus predicted all the results of the 2010 World Cup involving the German team as well as that of the final.
The Hermitage cats trace their history back to an order signed by Empress Elizabeth I in 1745 to find in the city of Kazan the "best and biggest 30 cats that are adept at catching mice and send them to her Majesty's court in Saint Petersburg."
They were replaced after the war, according to legend with a trainful of cats from all over the country.
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